Viscoelastic relaxations have been studied in thermotropic copolyesters synthesized by transesterification of diethyl p,p’-bibenzoate and different ratios of triethylene glycol (TEG) and 1,8-octanediol. A liquid crystal glass is obtained in these copolymers by fast quenching from the isotropic melt, as revealed by d.s.c. and X-ray measurements. Three relaxations, alpha, beta and gamma in order of decreasing temperature, appear in all the samples. The alpha relaxation is identified as the glass transition of the mesophase, and the results are compared with those obtained from d.s.c. measurements. The glass transition temperature of the mesophase of these copolymers shows a relationship with the composition similar to that for amorphous copolymers. The shape, intensity and temperature location of the alpha relaxation are very much dependent on the composition. More intense and sharper alpha peaks, shifted to lower temperatures, are obtained when the TEG content increases. The beta relaxation, associated with the carboxyl group, is also affected by the structure of the flexible oxyalkylene spacer. Finally, the gamma relaxation shifts to slightly lower temperatures when the TEG content increases.